Welcome to the forum jettabambino, I'm glad you are enjoying it. Rice Lake is one of many family friend lakes in the Lower Mainland. The Fraser Valley Trout Hatchery works very hard to ensure those such as yourself and the kids around you have an enjoyable fishing day when you are out there.
My advice to those who bring their kids to fishing is...
If you are bringing your kids or someone who is learning to fish, they become your responsibility. The quality of that fishing day is not based on how many fish you catch, but how much fun your companions have, how many fish they catch, how much they want to come back in the future, and how safe are they at the waters. While it is fantastic to see kids out fishing, too often they simply become a licence holder so the parent can have an extra daily quota.
Anyways, other lakes:
Alice Lake, Squamish
This is just past the town of Squamish on Sea to Sky. Shore fishing available, rainbow trout are abundant at times.
Sasamat Lake, Port Moody
There is a floating dock where it is popular for anglers. Pretty good trout fishing around sun down.
Buntzen Lake, Port Moody
Pretty lake, shore access is pretty good. The pier is a bit crowded most of the time as it is small. This lake contains bigger rainbow trout at times.
Lafarge Lake, Coquitlam
Small urban lake, good shore access, lots of casting room. Stocked with rainbow trout.
Whonnock Lake, Mission
Shore access is so so, better with a boat. Rainbow trout and crappies. It gets a bit busy with other users in the summer.
Mill Lake, Abbotsford
Another urban lake. Good shore access. A variety of species: Rainbow trout, crappies, largemouth bass, broodstock cutthroat trout up to 4lb.